Topological Data Analysis (TDA) has recently gained a great amount of popularity in the machine learning community. Apart from Persistent Homology, one of the more prominent methods has been the Mapper, originally proposed by [1]} due to its ability to provide a visualization of high-dimensional data. In short, the Mapper algorithm, as explained in the original paper (see [1]}) consists of a few steps. Given a point cloud \(X \in \mathbb {R}^d\) , one uses a filtration function \(f : \mathbb {R}^d \rightarrow \mathbb {R}^m\) , where \(m < d\) . This function, as stated by [1]}, "can be a function which reflects geometric properties of the data". Once reduced using the filtrations, the points are clustered using a clustering method of choice and mapped into overlapping bins forming vertices connected if they have common points, producing a graph that serves as an approximation of the Reeb graph (see [4]}).
